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Salsk061 [2.6K]

2 years ago

5

2 Emma buys 33 yards of blue fabric and some yellow fabric at a store. She buys a total of 53 yards of fabric. The equation 1 2

5333can be used to represent this situation, where y is the number of yards of yellow fabric she buys. How much yellow fabric does she buy?

1 answer:

Rus_ich [418]2 years ago

6 0

Step-by-step explanation:

your answer is 99

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Solve for X in 3x/10+x/5=15 PLEASE SHOW WORK

Firlakuza [10]

Answer:

x=30

Step-by-step explanation:

10(3x/10) + 10(x/5) = 10(15)

3x + 2x = 150

5x = 150

(5x)÷5 = (150)÷5

x = 30

5 0

3 years ago

Read 2 more answers

2) X and Y are jointly continuous with joint pdf

Nady [450]

From what I gather from your latest comments, the PDF is given to be

$f_{X,Y}(x,y)=\begin{cases}cxy&\text{for }0\le x,y \le1\\0&\text{otherwise}\end{cases}$

and in particular, <em>f(x, y)</em> = <em>cxy</em> over the unit square [0, 1]², meaning for 0 ≤ <em>x</em> ≤ 1 and 0 ≤ <em>y</em> ≤ 1. (As opposed to the unbounded domain, <em>x</em> ≤ 0 *and* <em>y</em> ≤ 1.)

(a) Find <em>c</em> such that <em>f</em> is a proper density function. This would require

$\displaystyle\int_0^1\int_0^1 cxy\,\mathrm dx\,\mathrm dy=c\left(\int_0^1x\,\mathrm dx\right)\left(\int_0^1y\,\mathrm dy\right)=\frac c{2^2}=1\implies \boxed{c=4}$

(b) Get the marginal density of <em>X</em> by integrating the joint density with respect to <em>y</em> :

$f_X(x)=\displaystyle\int_0^1 4xy\,\mathrm dy=(2xy^2)\bigg|_{y=0}^{y=1}=\begin{cases}2x&\text{for }0\le x\le 1\\0&\text{otherwise}\end{cases}$

(c) Get the marginal density of <em>Y</em> by integrating with respect to <em>x</em> instead:

$f_Y(y)=\displaystyle\int_0^14xy\,\mathrm dx=\begin{cases}2y&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}$

(d) The conditional distribution of <em>X</em> given <em>Y</em> can obtained by dividing the joint density by the marginal density of <em>Y</em> (which follows directly from the definition of conditional probability):

$f_{X\mid Y}(x\mid y)=\dfrac{f_{X,Y}(x,y)}{f_Y(y)}=\begin{cases}2x&\text{for }0\le x\le 1\\0&\text{otherwise}\end{cases}$

(e) From the definition of expectation:

$E[X]=\displaystyle\int_0^1\int_0^1 x\,f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=4\left(\int_0^1x^2\,\mathrm dx\right)\left(\int_0^1y\,\mathrm dy\right)=\boxed{\frac23}$

$E[Y]=\displaystyle\int_0^1\int_0^1 y\,f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=4\left(\int_0^1x\,\mathrm dx\right)\left(\int_0^1y^2\,\mathrm dy\right)=\boxed{\frac23}$

$E[XY]=\displaystyle\int_0^1\int_0^1xy\,f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=4\left(\int_0^1x^2\,\mathrm dx\right)\left(\int_0^1y^2\,\mathrm dy\right)=\boxed{\frac49}$

(f) Note that the density of <em>X</em> | <em>Y</em> in part (d) identical to the marginal density of <em>X</em> found in (b), so yes, <em>X</em> and <em>Y</em> are indeed independent.

The result in (e) agrees with this conclusion, since E[<em>XY</em>] = E[<em>X</em>] E[<em>Y</em>] (but keep in mind that this is a property of independent random variables; equality alone does not imply independence.)

8 0

3 years ago

If f(6) if f(x)=x^2 / 3 + x

MakcuM [25]

Answer:

1) If the function is $f(x)=\frac{x^{2}}{(3+x)}$ , $f(6)=4$

2) If the function is $f(x)=x^{(2/3)}+x$ , $f(6)=9.30$

3) If the function is $f(x)=\frac{x^{2}}{3}+x$ , $f(6)=18$

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

f(6) means that you must substitute x=6 into the function above.

1. If the given the function $f(x)=\frac{x^{2}}{(3+x)}$ , you obtain:

$f(6)=\frac{6^{2}}{(3+6)}=4$

2. If the function is $f(x)=x^{(2/3)}+x$

Then:

$f(6)=6^{(2/3)}+6=9.30$

3. If the function is $f(x)=\frac{x^{2}}{3}+x$

Then:

$f(6)=\frac{6^{2}}{3}+6=18$

6 0

2 years ago

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The baby giraffe weighed 132 pounds at birth. He gained weight at a steady rate for the first 7 months until his weight reached

marusya05 [52]

Answer:

the giraffe gained 58 pounds each month.

Step-by-step explanation:

do 538-132 then do 406÷7. you will get 58.

hope this helps!

8 0

3 years ago

I need help with a math problem 6838 multiplied by 2830 then that answer divided by 2

Tresset [83]

Answer:

9675770

Step-by-step explanation:

Hope this helps

7 0

3 years ago

Read 2 more answers